NCERT Notes for Class 10 Maths Chapter 8 Introduction to Trigonometry
Class 10 Maths Chapter 8 Introduction to Trigonometry Notes
Chapter Name  Introduction to Trigonometry Notes 
Class  CBSE Class 10 
Textbook Name  NCERT Mathematics Class 10 
Related Readings 

Trigonometry
To find the distances and heights we can use the mathematical techniques, which come under the Trigonometry. It shows the relationship between the sides and the angles of the triangle. Generally, it is used in the case of a right angle triangle.
Trigonometric Ratios
In a right angle triangle, the ratio of its side and the acute angles is the trigonometric ratios of the angles.
In this right angle triangle ∠B = 90°. If we take ∠A as acute angle then: 
 AB is the base, as the side adjacent to the acute angle.
 BC is the perpendicular, as the side opposite to the acute angle.
 Ac is the hypotenuse, as the side opposite to the right angle.
Trigonometric ratios with respect to ∠A
Ratio 
Formula 
Short form 
Value 
Sin A 
P/H 
BC/AC 

Cos A 
B/H 
AB/AC 

Tan A 
P/B 
BC/AB 

Cosec A 
H/P 
AC/BC 

Sec A 
H/B 
AC/AB 

Cot A 
B/P 
AB/BC 
Remark
 If we take ∠C as acute angle then BC will be base and AB will be perpendicular. Hypotenuse remains the same i.e. AC. So, the ratios will be according to that only.
 If the angle is same then the value of the trigonometric ratios of the angles remain the same whether the length of the side increases or decreases.
 In a right angle triangle, the hypotenuse is the longest side so sin A or cos A will always be less than or equal to 1 and the value of sec A or cosec A will always be greater than or equal to 1.
Reciprocal relation between Trigonometric Ratios
Cosec A, sec A, and cot A are the reciprocals of sin A, cos A, and tan A respectively.
Quotient Relation
Trigonometric Ratios of Some Specific Angles
Use of Trigonometric Ratios and Table in Solving Problems
Example: Find the lengths of the sides BC and AC in ∆ ABC, rightangled at B where AB = 25 cm and ∠ACB = 30°, using trigonometric ratios.
Solution
To find the length of the side BC, we need to choose the ratio having BC and the given side AB. As we can see that BC is the side adjacent to angle C and AB is the side opposite to angle C, therefore
AC = 50 cm
Trigonometric Ratios of Complementary Angles
If the sum of two angles is 90° then, it is called Complementary Angles. In a rightangled triangle, one angle is 90 °, so the sum of the other two angles is also 90° or they are complementary angles.so the trigonometric ratios of the complementary angles will be 
sin (90° – A) = cos A,
cos (90° – A) = sin A,
tan (90° – A) = cot A,
cot (90° – A) = tan A,
sec (90° – A) = cosec A,
cosec (90° – A) = sec A
Trigonometric Identities (Pythagoras Identity)
An equation is said to be a trigonometric identity if it contains trigonometric ratios of an angle and satisfies it for all values of the given trigonometric ratios.
In ∆PQR, right angled at Q, we can say that
PQ^{2} + QR^{2} = PR^{2}
Divide each term by PR^{2}, we get
(sin R)^{2} + (cos R)^{2} = 1
sin^{2} R + cos^{2} R =1
Likewise other trigonometric identities can also be proved. So the identities are
sin^{2} R + cos^{2} R = 1
1 + tan^{2} R = sec^{2} R
cot^{2} R + 1 = cosec^{2} R
How to solve the problems related to trigonometric ratios and identities?
Prove that
Hence, L.H.S = R.H.S